Answers
[tex]\boxed{\boxed{\pink{\sf \leadsto Hence \ the \ Inverse \ of \ the \ given \ function \ is \ x^2+2x-4 .}}}[/tex]
Step-by-step explanation:A function is given to us , and we need to find its inverse. So the function is ,
[tex]\bf\implies f(x) = \sqrt{x + 5 } - 1 [/tex]
So , firstly replace x with y in the given function and then solve for y to get its inverse . Taking the given function ,
[tex]\bf \implies f(x) = \sqrt{x+5}-1\\\\\bf\implies y = \sqrt{x+5}-1 \\\\\bf\implies x = \sqrt{y+5}-1 \:\:\bigg\lgroup \red{\sf Replacing \ x \ with \ y .} \bigg\rgroup \\\\\bf\implies x + 1 = \sqrt{y+5}\\\\\bf\implies y+5 = (x+1)^2 \\\\\bf\implies y+5 = x^2+1 +2x \\\\\bf\implies y = x^2+1-5+2x \\\\\bf\implies y = x^2-4+2x \\\\\bf\implies \boxed{\red{\bf f^{-1}(x)= x^2+2x - 4 }}[/tex]
Here I have also attached the graph of , x² + 2x - 4 and √(x+5) - 1. Here blue graph is of √(x+5) - 1 & red of x²+2x-4.
Hence the inverse f -¹(x) of the given function is x² + 2x - 4 .
Related Questions
What is the value of X?
PLEASE HELP
Answers
Answer:
23
Step-by-step explanation:
19=x-4
x=23
Determine the shortest distance from the point (5, 2) to the line represented by y=2x+1.
Answers
Answer:
5 and 6 because it is the nearest
David has 768 gumballs. He decides to give 95% of them to a friend as a birthday present. How many gumballs does David give away?
Answers
Answer:
729.6
Step-by-step explanation:
to much
Help me out with this please??? someone??? A model airplane is built with a wing span of 23 inches. The actual wingspan is 92 feet. What is the scale of the model???
Answers
Answer:
The scale is five. you do 90 divided by 18.
on a graph there are two points (0,3) and (8,0) what is the proper equation
Answers
Answer:
The line equation of the line is:
[tex]y=-\frac{3}{8}x+3[/tex]Step-by-step explanation:
Given the two points
(0,3)(8,0)Finding the slope between (0,3) and (8,0)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:0\right)[/tex]
[tex]m=\frac{0-3}{8-0}[/tex]
[tex]m=-\frac{3}{8}[/tex]
Therefore, the slope of the line: m = -3/8
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -3/8 and the point (0,3)
[tex]y-3=-\frac{3}{8}\left(x-0\right)[/tex]
[tex]y-3=-\frac{3}{8}x[/tex]
Add 3 to both sides
[tex]y-3+3=-\frac{3}{8}x+3[/tex]
Simplify
[tex]y=-\frac{3}{8}x+3[/tex]
Therefore, the line equation of the line is:
[tex]y=-\frac{3}{8}x+3[/tex]A middle-school art teacher, Ms. Velez, and her students are turning the school’s gymnasium into a student art museum for the day.
Ms. Velez types a program for the event and writes: "The most popular art museum in the world, the Louvre, has approximately 9,300,000 visitors each year. About 1,900,000 of those visitors are young people age 18 to 25."
1) How would you write the two numbers above in scientific notation? (2 points)
2) BONUS: Approximately what percent of visitors to the Louvre are young people?
Answers
Answer:19 to the 5th power
Step-by-step explanation:
U got to count all the zeros and that will be the number u put on top plus 19
The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius holds 1½ pints, how many gallons will a similar can with a 24-inch radius hold?
Answers
Answer:
The second similar can with a radius of 24-inch radius will hold 12 gallons
Step-by-step explanation:
The given parameters are;
The volumes of the cylindrical can ∝ (The radius of the cans)³
The volume of first can, V₁ = 1¹/₂ pints
The radius of the first can, r₁ = 6-inch
The radius of the second can, r₂ = 24-inch
Therefore, we have;
V ∝ r³
V = k × r³
∴ 1¹/₂ pints ∝ (6 in.)³
1¹/₂ pints = 43.3125 in³
∴ 43.3125 in³ = k × 216 in.³
The constant of proportionality, k = 43.3125/216 = 0.2005208333
Therefore, we have for the second can, we have;
V₂ = k × r₂³ = 43.3125/216 × (24 in.)³ = 2772 in.³
The volume of the second can = 2772 in.³
1 in.³ = 0.004329 gallons
∴ 2772 in.³ = 2772 × 0.004329 gallons = 12 gallons
Therefore, the volume the second similar can with a 24-inch radius will hold = 12 gallons.
Darren has just unplugged his fridge so it can defrost. Thefreezer is at 17 degrees and warms up at 11 degrees an hour.The fridge part is at 23 degrees and rises 8 degrees per hour.How many hours will it take for both the fridge and thefreezer to be the same temperature? What is thetemperature change in that time span?
Answers
Answer:
im not sure
Step-by-step explanation:
wish i could help!! :((
bUT THANKS for the pointssssssss
Answer:
they intercept at (2,39)
Step-by-step explanation:
so, the starting point is the y int, and the rate it warms up is the slope so you need to create an equation that follows y=mx+b, then you can use a graphing calculator like desmos, to graph the equation.
the equations would be y=11x+17 and 8x+23, x represents hours.
10 Points + Brainliest to first correct answer. Please give explanation for Brainliest. Any fake answers will be reported and deleted.
Which diagram best shows how fraction bars can be used to evaluate 1/2 divided by 1/4?
Answers
the second one is correct
1. A triangle has a base of 8km and height of 3km. What is the area of the triangle?
2. What is the area of a triangle with a base of 4 inches and a height of 9 inches?
Help would be much appreciated
Answers
Answer:
1. 12 square kilometers
2.18 square inches
Step-by-step explanation:
To find the area of a square you multiply the base and the height. Then you divide it by 2. 8 times 3 divided by 2 is 12. 4 times 9 divided by 2 is 18. Hope this helps!
Solve for x. show work. 8+b/-4=5
Answers
Answer:
b=12
Step-by-step explanation:
What is the slope of a line parallel to the line whose equation is 18x - 3y = -45 fully reduce your answer
Answers
Solve 3x - 4 ≤ 2 or 2x + 11 ≥ -1.
please help
Answers
Answer:
x≤2 or x≥-6
Step-by-step explanation:
Isolate the variables on both equations
3x-4≤2
3x≤6
x≤2
2x+11≥-1
2x≥-12
x≥-6
What is 0.82 as a fraction in simplest form?
(I also need the work if not its ok!)
Answers
Answer:
f 41/50
Step-by-step explanation:
A gardening company sells clay flower pots and plastic flower pots. There must be at least 2 pots in each shipment, but there cannot be more than 8 in a shipment. Additionally, the shipment must weigh less than 100 lbs. Each shipment container weighs 20 lbs., and there is 1 lb. of packing material. A clay flower pot weighs 15 lbs., whereas a plastic flower pot weighs 7.5 lbs.
(A) Write a system of inequalities that represent the constraints on the number of pots that can be included in one shipment.
Answers
The system of inequalities can be obtained from the given information
on the allowable weights and number of pots.
The correct responses:
The system of inequalities that represent the constraint on the number
of pots that can be included in one shipment are;
2 ≤ x + y ≤ 815·x + 7.5·y ≤ 79 lbs.Methods used to find the system of inequalitiesThe inequality that represents the number total number of clay, T, in each shipment is 2 ≤ T ≤ 8
The inequality that represents weight of each shipment is w < 100 lbs
The weight of each shipment container = 20 lbs
The weight of the packing material = 1 lb
Therefore;
The maximum weight of the flower pots = 100 lbs - 21 lbs = 79 lbsThe weight of each clay flower pot = 15 lbs
The weight of each plastic flower pot = 7.5 lbs
Let "x" represent the number of clay flower pot included in one shipment
and let "y" represent the number of plastic flower pot included in one
shipment, we have;
The system of inequalities that represent the constraint on the number of pots that can be included in one shipment are as follows;
2 ≤ x + y ≤ 815·x + 7.5·y ≤ 79 lbs.Learn more about inequalities here:
https://brainly.com/question/10868639
We will find the system of inequalities:
C*15 lb + P*7.5lb < 79 lb
2 ≤ P + C ≤ 8
How to write a system of inequalities?
First, we need to define the variables that we will be using, these are:
C = number of clay pots.P = number of plastic pots.From the first restriction, we have that:
2 ≤ P + C ≤ 8
The other restriction says that the weight must be less than 100lbs:
W < 100lbs
Where the weight is:
W = C*15 lb + P*7.5lb + 20lb + 1lb
Where 20lb is the weight of the container and 1lb is the weight of the packing material, then we have:
C*15 lb + P*7.5lb + 20lb + 1lb < 100lb
We can subtract 21 lb in both sides to get:
C*15 lb + P*7.5lb < 100 lb - 21 lb
C*15 lb + P*7.5lb < 79 lb
So we got our two inequalities, then the system is:
C*15 lb + P*7.5lb < 79 lb
2 ≤ P + C ≤ 8
If you want to learn more about systems of inequalities, you can read:
https://brainly.com/question/9774970
4(10s) – 20 – 50s – 12 + 4s PLEASE HELP AND EXPLAIN
Answers
40s-20-50s-12+4s
-6s+-32
help???????
dhdjdjmsjd
Answers
Answer:
1/2 over 7/8
Step-by-step explanation:
becauseim smartt
Answer:
the bridge is 90ft long.
Step-by-step explanation:
3/18=15/x
solve for x
use reciprocals to get x as numerator for easier calculation
18/3=x/15
270/3=x
x=90ft
A boy at an amusement park has 38 ride tickets. Each ride on the roller coaster costs 5 tickets. After riding the roller coaster as many times as he can,how many tickets will the boy have left?
Answers
Answer:
He will expend 35 tickets for 7 rides. 3 tickets are left.
Step-by-step explanation:
Giving the following information:
Number of tickets= 38
Tickets per ride= 5
To calculate the number of rides he can make, we need to use the following formula:
Number of rides= number of tickets / tickets per ride
Number of rides= 38/5
Number of rides= 7.6 = 7 rides
He will expend 35 tickets for 7 rides. 3 tickets are left.
Please please please help!!!!!
Answers
Answer:
12 sheets
Step-by-step explanation:
Answer:
12 sheets
Step-by-step explanation:
Prove the Isosceles Triangle Theorem as a paragraph proof.
Answers
Answer:
Reflexive Property
SAS
<C
find the value of x
x=
Answers
Answer:
x = 4
Step-by-step explanation:
Since BD is an angle bisector then it divides the opposite side into segments that are proportional to the other 2 sides, that is
[tex]\frac{BA}{BC}[/tex] = [tex]\frac{AD}{CD}[/tex] , substitute values
[tex]\frac{x}{6}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3x = 12 ( divide both sides by 3 )
x = 4
Resuelve por el perímetro.
5 cm
8 cm
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Answer:
5cm
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A car rental company charges $26 per day for a rented car and $0.50 for every mile driven. A second car rental company charges $18 per
day and $0.75 for every mile driven. What is the number of miles at which both companies charge the same amount for a one-day rental?
O A 24 miles
OB. 32 miles
C. 42 miles
o D. 44 miles
Answers
The sum of two integers is 5. Their difference is 11. What are
the two integers?
A) 3 and 14
B) -3 and 8
C)2 and 3
D) -14 and - 3
Answers
Answer:a
Step-by-step explanation:
A model is made of an Airbus A300 aeroplane.
The length of the model is 36 cm.
The length of the real aeroplane is 54 m.
Answers
Answer:
Since the Airbus A300 model airplane was made to scale, measuring 36 centimeters, while the real airplane measures 54 meters, to determine the scale ratio between both planes, the following calculation must be performed:
36cm = 0.36m
0.36 = 1
54 = X
54 x 1 / 0.36 = X
150 = X
Therefore, the scale ratio between the model and the real plane is 150:1.
In the diagram AB is parallel to CD. What is the value of X
Answers
Answer:
B) 120
Step-by-step explanation:
There are 20 consecutive even numbers. How much bigger is the sum of the larger 10 ones than the sum of the smaller ones?
Answers
Answer:
The answer is 200
Step-by-step explanation:
easy 10 points, math underline. photo below
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
PLEASE HELP !!! ASAPPPP Select the statement that describes this expression: 10 + fraction 1 over 4x (5 + 3) − 3.
O 10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3 fraction.
O 1 over 4 of 10 times the sum of 5 and 3, minus 3
O 3 more than 3 plus 5 multiplied by fraction 1 over 4, then add 10
O 10 times fraction 1 over 4 plus 3 and 5, minus 3
Answers
Answer:
I think its the first one...
Step-by-step explanation:
Answer:
First one
Step-by-step explanation:
the spinner below is spun then the a month of the year is randomly selected. Find each probability
Answers
Answer:
I think the answer is 0.3
Step-by-step explanation:
Sorry if am wrong.
Answer:
Step-by-step explanation:
P (blue) fraction = 2/8 decimal=.25 percent=25%
P(purple) fraction=0/8 decimal=0 percent =0%
P(not green) fraction=5/8 decimal=.625 percent= 62.5%
P(not brown) fraction=8/8 decimal=1 percent =100%
2)Refer to the table on air travel selected airports. Suppose a flight that arrived at El Centro is selected at random. What is the probability that the flight did not arrive on time? write your answer as a fraction, decimal and percent.
80% on time so 20% are not on time
20/100 ÷ 20 =1/5
20%, .2, 1/5
3)The spinner has 8 sectors labeled with letters. Each sector of the spinner below is the same size, as shown.
If the arrow is spun 400 times , how many times would it be expected to land on a sector labeled B?
[tex]\frac{B}{Total} \\\frac{3}{8} =\frac{x}{400\\}[/tex]
A)50 C)150
B)100 D)250
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